Question

Find the value of x.

m<2= x + 85​

Answer 1

Answer: x = -9

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Step-by-step explanation:

Refer to the diagram below.

I've added the points A,B,C,D,E, and F to help set up the angles.

I've marked angle 2 as the variable y, which is angle DBA. I've also added in the variable w to help fill out triangle DBA. Those two remaining angles are congruent due to the congruent sides AB = DB. They are the base angles. Triangle DBA is isosceles.

Right next to angle DAB is angle CAB. These two angles combine to form the 90 degree angle. So that's where the 90-w comes from when setting up angle CAB. We have another isosceles triangle, so angles CAB and ACB are congruent.

Next, we can see that angles ACB and ECF are vertical angles. That makes them congruent and we can solve for w like so:

angle ACB = angle ECF

90 - w = 38

-w = 38-90

-w = -52

w = 52

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Now focus on triangle DBA again. The three angles add to 180, so,

w+y+w = 180

2w+y = 180

y = 180-2w

y = 180-2*52

y = 180-104

y = 76

This is the measure of angle 2. We have one more step left.

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Since we now know the measure of angle 2, we can use this to find x

angle 2 = 76 degrees

angle 2 = x+85

x+85 = 76

x = 76 - 85

x = -9

Answer 2

• x = - 9

Step-by-step explanation:

Solution 1

The both triangles are marked as isosceles.

The bottom triangle

Missing angles are same:

• 1/2(180 - x - 85) = 1/2(95 - x)

The top triangle

The equal angles measure 38° as one of them is vertically opposite to 38° angle.

On the other hand same angle is complementary with the one we found above (together forming a right angle).

So we have:

• 1/2(95 - x) + 38 = 90
• 1/2(95 - x) = 52
• 95 - x = 104
• x = 95 - 104
• x = - 9

Solution 2

The angle 2 is the exterior angle of the top triangle.

The non-adjacent interior angles are equal to each other and same as vertical angle of the top vertex, 38°.

• m∠2 = 2*38° = 76°

Also we have:

• m∠2 = x + 85

Compare and solve for x:

• x + 85 = 76
• x = 76 - 85
• x = -9